• This event has passed.

# Hong Liu, A proof of Mader’s conjecture on large clique subdivisions in $C_4$-free graphs

## December 12 Thursday @ 4:30 PM - 5:30 PM

Room 1401, Bldg. E6-1, KAIST

### Speaker

Hong Liu
Mathematics Institute, University of Warwick, UK
http://homepages.warwick.ac.uk/staff/H.Liu.9/
Given any integers $s,t\geq 2$, we show there exists some $c=c(s,t)>0$ such that any $K_{s,t}$-free graph with average degree $d$ contains a subdivision of a clique with at least $cd^{\frac{1}{2}\frac{s}{s-1}}$ vertices. In particular, when $s=2$ this resolves in a strong sense the conjecture of Mader in 1999 that every $C_4$-free graph has a subdivision of a clique with order linear in the average degree of the original graph. In general, the widely conjectured asymptotic behaviour of the extremal density of $K_{s,t}$-free graphs suggests our result is tight up to the constant $c(s,t)$. This is joint work with Richard Montgomery.

## Details

Date:
December 12 Thursday
Time:
4:30 PM - 5:30 PM
Event Category:
Event Tags:

## Venue

Room 1401, Bldg. E6-1, KAIST

## Organizer

Jaehoon Kim (김재훈)
Email: